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What you should do is store the scale where you are at for each detection. Then transforming should be rather easy right. Imagine you have the following.
X and Y coordinates (center of bounding box) at scale 1/2 of the original. This means that you should multiply with the inverse of the scale to get the location in the original, which would be 2X, 2Y (again for the bounxing box center).
So first transform the center of the bounding box, than calculate the width and height of your bounding box in the original, again by multiplying with the inverse. Then from the center, your box will be +-width_double/2 and +-height_double/2.
